Question

Consider the simple linear regression model: Suppose that the estimate of B1 based on a sample of 55 individuals is 2.3 and the corresponding standard error is 0.96. Test the null hypothesis H0: β1-0 vs HA: A 0 at the α-0.05 level and provide the corresponding p-value.

Answer 1

$H_0: \beta_1 = 0$

$H_A: \beta_1 \ne 0$

Significance level $\alpha$ = 0.05

Degree of freedom = n - 2 = 55 - 2 = 53

Test statistic, t = (Estimated coefficient - Hypothesized value) / Standard error

= (2.3 - 0) / 0.96 = 2.3958

P(t > 2.3958) for df = 53 is  0.0101

For two tail test, p-value = 2 * 0.0101 = 0.0202

Since, p-value is less than $\alpha$, we reject null hypothesis H0 and conclude that there is statistical significant evidence that  $\beta_1 \ne 0$.